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MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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
Transcribed Image Text:The Venn diagram below shows the 8 students in Mr. Parker’s class. The diagram shows the memberships for the Volleyball Club and the Spanish Club.
Note that "Austin" is outside the circles since he is not a member of either club.
One student from the class is randomly selected.
Let \( A \) denote the event "the student is in the Volleyball Club."
Let \( B \) denote the event "the student is in the Spanish Club."
Answer each part below. If necessary, consult a list of formulas.
**Venn Diagram Explanation:**
- **Volleyball Club**: Circle on the left with members: Mai, Jose, Felipe
- **Spanish Club**: Circle on the right with members: Jose, Felipe, Keith, Keiko, Lisa, Lamar
- **Overlap (Both Clubs)**: Jose, Felipe
- **Outside Both Circles**: Austin
**Task (a):** Find the probabilities of the events below. Write each answer as a single fraction.
- \( P(A) = \) \(\_\)
- \( P(B) = \) \(\_\)
- \( P(A \text{ and } B) = \) \(\_\)
- \( P(A \text{ or } B) = \) \(\_\)
- \( P(A) + P(B) - P(A \text{ and } B) = \) \(\_\)
**Task (b):** Select the probability that is equal to \( P(A) + P(B) - P(A \text{ and } B) \).
- \( \circ P(A) \)
- \( \circ P(A \text{ and } B) \)
- \( \circ P(A \text{ or } B) \)
- \( \circ P(B) \)
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